RNA quality control factors nucleate Clr4/SUV39H and trigger constitutive heterochromatin assembly.

In eukaryotes, the Suv39 family of proteins tri-methylate lysine 9 of histone H3 (H3K9me) to form constitutive heterochromatin. However, how Suv39 proteins are nucleated at heterochromatin is not fully described. In the fission yeast, current models posit that Argonaute1-associated small RNAs (sRNAs) nucleate the sole H3K9 methyltransferase, Clr4/SUV39H, to centromeres. Here, we show that in the absence of all sRNAs and H3K9me, the Mtl1 and Red1 core (MTREC)/PAXT complex nucleates Clr4/SUV39H at a heterochromatic long noncoding RNA (lncRNA) at which the two H3K9 deacetylases, Sir2 and Clr3, also accumulate by distinct mechanisms. Iterative cycles of H3K9 deacetylation and methylation spread Clr4/SUV39H from the nucleation center in an sRNA-independent manner, generating a basal H3K9me state. This is acted upon by the RNAi machinery to augment and amplify the Clr4/H3K9me signal at centromeres to establish heterochromatin. Overall, our data reveal that lncRNAs and RNA quality control factors can nucleate heterochromatin and function as epigenetic silencers in eukaryotes.

Structural Insights into Yeast Telomerase Recruitment to Telomeres.

Telomerase maintains chromosome ends from humans to yeasts. Recruitment of yeast telomerase to telomeres occurs through its Ku and Est1 subunits via independent interactions with telomerase RNA (TLC1) and telomeric proteins Sir4 and Cdc13, respectively. However, the structures of the molecules comprising these telomerase-recruiting pathways remain unknown. Here, we report crystal structures of the Ku heterodimer and Est1 complexed with their key binding partners. Two major findings are as follows: (1) Ku specifically binds to telomerase RNA in a distinct, yet related, manner to how it binds DNA; and (2) Est1 employs two separate pockets to bind distinct motifs of Cdc13. The N-terminal Cdc13-binding site of Est1 cooperates with the TLC1-Ku-Sir4 pathway for telomerase recruitment, whereas the C-terminal interface is dispensable for binding Est1 in vitro yet is nevertheless essential for telomere maintenance in vivo. Overall, our results integrate previous models and provide fundamentally valuable structural information regarding telomere biology.

Assembly-mediated activation of the SIR2-HerA supramolecular complex for anti-phage defense.

SIR2-HerA, a bacterial two-protein anti-phage defense system, induces bacterial death by depleting NAD+ upon phage infection. Biochemical reconstitution of SIR2, HerA, and the SIR2-HerA complex reveals a dynamic assembly process. Unlike other ATPases, HerA can form various oligomers, ranging from dimers to nonamers. When assembled with SIR2, HerA forms a hexamer and converts SIR2 from a nuclease to an NAD+ hydrolase, representing an unexpected regulatory mechanism mediated by protein assembly. Furthermore, high concentrations of ATP can inhibit NAD+ hydrolysis by the SIR2-HerA complex. Cryo-EM structures of the SIR2-HerA complex reveal a giant supramolecular assembly up to 1 MDa, with SIR2 as a dodecamer and HerA as a hexamer, crucial for anti-phage defense. Unexpectedly, the HerA hexamer resembles a spiral staircase and exhibits helicase activities toward dual-forked DNA. Together, we reveal the supramolecular assembly of SIR2-HerA as a unique mechanism for switching enzymatic activities and bolstering anti-phage defense strategies.

Multiple enzymatic activities of a Sir2-HerA system cooperate for anti-phage defense.

In response to the persistent exposure to phage infection, bacteria have evolved diverse antiviral defense mechanisms. In this study, we report a bacterial two-component defense system consisting of a Sir2 NADase and a HerA helicase. Cryo-electron microscopy reveals that Sir2 and HerA assemble into a ∼1 MDa supramolecular octadecamer. Unexpectedly, this complex exhibits various enzymatic activities, including ATPase, NADase, helicase, and nuclease, which work together in a sophisticated manner to fulfill the antiphage function. Therefore, we name this defense system "Nezha" after a divine warrior in Chinese mythology who employs multiple weapons to defeat enemies. Our findings demonstrate that Nezha could sense phage infections, self-activate to arrest cell growth, eliminate phage genomes, and subsequently deactivate to allow for cell recovery. Collectively, Nezha represents a paradigm of sophisticated and multifaceted strategies bacteria use to defend against viral infections.

RNA Polymerase I Activators Count and Adjust Ribosomal RNA Gene Copy Number.

Ribosome is the most abundant RNA-protein complex in a cell, and many copies of the ribosomal RNA gene (rDNA) have to be maintained. However, arrays of tandemly repeated rDNA genes can lose the copies by intra-repeat recombination. Loss of the rDNA copies of Saccharomyces cerevisiae is counteracted by gene amplification whereby the number of rDNA repeats stabilizes around 150 copies, suggesting the presence of a monitoring mechanism that counts and adjusts the number. Here, we report that, in response to rDNA copy loss, the upstream activating factor (UAF) for RNA polymerase I that transcribes the rDNA is released and directly binds to a RNA polymerase II-transcribed gene, SIR2, whose gene products silence rDNA recombination, to repress. We show that the amount of UAF determines the rDNA copy number that is stably maintained. UAF ensures rDNA production not only by rDNA transcription activation but also by its copy-number maintenance.

The probability of epidemic burnout in the stochastic SIR model with vital dynamics.

We present an approach to computing the probability of epidemic "burnout," i.e., the probability that a newly emergent pathogen will go extinct after a major epidemic. Our analysis is based on the standard stochastic formulation of the Susceptible-Infectious-Removed (SIR) epidemic model including host demography (births and deaths) and corresponds to the standard SIR ordinary differential equations (ODEs) in the infinite population limit. Exploiting a boundary layer approximation to the ODEs and a birth-death process approximation to the stochastic dynamics within the boundary layer, we derive convenient, fully analytical approximations for the burnout probability. We demonstrate-by comparing with computationally demanding individual-based stochastic simulations and with semi-analytical approximations derived previously-that our fully analytical approximations are highly accurate for biologically plausible parameters. We show that the probability of burnout always decreases with increased mean infectious period. However, for typical biological parameters, there is a relevant local minimum in the probability of persistence as a function of the basic reproduction number [Formula: see text]. For the shortest infectious periods, persistence is least likely if [Formula: see text]; for longer infectious periods, the minimum point decreases to [Formula: see text]. For typical acute immunizing infections in human populations of realistic size, our analysis of the SIR model shows that burnout is almost certain in a well-mixed population, implying that susceptible recruitment through births is insufficient on its own to explain disease persistence.

Minimal requirements for the epigenetic inheritance of engineered silent chromatin domains.

Mechanisms enabling genetically identical cells to differentially regulate gene expression are complex and central to organismal development and evolution. While gene silencing pathways involving DNA sequence-specific recruitment of histone-modifying enzymes are prevalent in nature, examples of sequence-independent heritable gene silencing are scarce. Studies of the fission yeast Schizosaccharomyces pombe indicate that sequence-independent propagation of heterochromatin can occur but requires numerous multisubunit protein complexes and their diverse activities. Such complexity has so far precluded a coherent articulation of the minimal requirements for heritable gene silencing by conventional in vitro reconstitution approaches. Here, we take an unconventional approach to defining these requirements by engineering sequence-independent silent chromatin inheritance in budding yeast Saccharomyces cerevisiae cells. The mechanism conferring memory upon these cells is remarkably simple and requires only two proteins, one that recognizes histone H3 lysine 9 methylation (H3K9me) and catalyzes the deacetylation of histone H4 lysine 16 (H4K16), and another that recognizes deacetylated H4K16 and catalyzes H3K9me. Together, these bilingual "read-write" proteins form an interdependent positive feedback loop that is sufficient for the transmission of DNA sequence-independent silent information over multiple generations.

Sir3 heterochromatin protein promotes non-homologous end joining by direct inhibition of Sae2.

Heterochromatin is a conserved feature of eukaryotic chromosomes, with central roles in gene expression regulation and maintenance of genome stability. How heterochromatin proteins regulate DNA repair remains poorly described. In the yeast Saccharomyces cerevisiae, the silent information regulator (SIR) complex assembles heterochromatin-like chromatin at sub-telomeric chromosomal regions. SIR-mediated repressive chromatin limits DNA double-strand break (DSB) resection, thus protecting damaged chromosome ends during homologous recombination (HR). As resection initiation represents the crossroads between repair by non-homologous end joining (NHEJ) or HR, we asked whether SIR-mediated heterochromatin regulates NHEJ. We show that SIRs promote NHEJ through two pathways, one depending on repressive chromatin assembly, and the other relying on Sir3 in a manner that is independent of its heterochromatin-promoting function. Via physical interaction with the Sae2 protein, Sir3 impairs Sae2-dependent functions of the MRX (Mre11-Rad50-Xrs2) complex, thereby limiting Mre11-mediated resection, delaying MRX removal from DSB ends, and promoting NHEJ.

Phylogenetic inference of inter-population transmission rates for infectious diseases.

Estimating transmission rates is a challenging yet essential aspect of comprehending and controlling the spread of infectious diseases. Various methods exist for estimating transmission rates, each with distinct assumptions, data needs, and constraints. This study introduces a novel phylogenetic approach called transRate, which integrates genetic information with traditional epidemiological approaches to estimate inter-population transmission rates. The phylogenetic method is statistically consistent as the sample size (i.e. the number of pathogen genomes) approaches infinity under the multi-population susceptible-infected-recovered model. Simulation analyses indicate that transRate can accurately estimate the transmission rate with a sample size of 200 ~ 400 pathogen genomes. Using transRate, we analyzed 40,028 high-quality sequences of SARS-CoV-2 in human hosts during the early pandemic. Our analysis uncovered significant transmission between populations even before widespread travel restrictions were implemented. The development of transRate provides valuable insights for scientists and public health officials to enhance their understanding of the pandemic's progression and aiding in preparedness for future viral outbreaks. As public databases for genomic sequences continue to expand, transRate is increasingly vital for tracking and mitigating the spread of infectious diseases.

ARV1 deficiency induces lipid bilayer stress and enhances rDNA stability by activating the unfolded protein response in Saccharomyces cerevisiae.

The stability of ribosomal DNA (rDNA) is maintained through transcriptional silencing by the NAD+-dependent histone deacetylase Sir2 in Saccharomyces cerevisiae. Alongside proteostasis, rDNA stability is a crucial factor regulating the replicative lifespan of S. cerevisiae. The unfolded protein response (UPR) is induced by misfolding of proteins or an imbalance of membrane lipid composition and is responsible for degrading misfolded proteins and restoring endoplasmic reticulum (ER) membrane homeostasis. Recent investigations have suggested that the UPR can extend the replicative lifespan of yeast by enhancing protein quality control mechanisms, but the relationship between the UPR and rDNA stability remains unknown. In this study, we found that the deletion of ARV1, which encodes an ER protein of unknown molecular function, activates the UPR by inducing lipid bilayer stress. In arv1Δ cells, the UPR and the cell wall integrity pathway are activated independently of each other, and the high osmolarity glycerol (HOG) pathway is activated in a manner dependent on Ire1, which mediates the UPR. Activated Hog1 translocates the stress response transcription factor Msn2 to the nucleus, where it promotes the expression of nicotinamidase Pnc1, a well-known Sir2 activator. Following Sir2 activation, rDNA silencing and rDNA stability are promoted. Furthermore, the loss of other ER proteins, such as Pmt1 or Bst1, and ER stress induced by tunicamycin or inositol depletion also enhance rDNA stability in a Hog1-dependent manner. Collectively, these findings suggest that the induction of the UPR enhances rDNA stability in S. cerevisiae by promoting the Msn2-Pnc1-Sir2 pathway in a Hog1-dependent manner.

Mot1, Ino80C, and NC2 Function Coordinately to Regulate Pervasive Transcription in Yeast and Mammals.

Pervasive transcription initiates from cryptic promoters and is observed in eukaryotes ranging from yeast to mammals. The Set2-Rpd3 regulatory system prevents cryptic promoter function within expressed genes. However, conserved systems that control pervasive transcription within intergenic regions have not been well established. Here we show that Mot1, Ino80 chromatin remodeling complex (Ino80C), and NC2 co-localize on chromatin and coordinately suppress pervasive transcription in S. cerevisiae and murine embryonic stem cells (mESCs). In yeast, all three proteins bind subtelomeric heterochromatin through a Sir3-stimulated mechanism and to euchromatin via a TBP-stimulated mechanism. In mESCs, the proteins bind to active and poised TBP-bound promoters along with promoters of polycomb-silenced genes apparently lacking TBP. Depletion of Mot1, Ino80C, or NC2 by anchor away in yeast or RNAi in mESCs leads to near-identical transcriptome phenotypes, with new subtelomeric transcription in yeast, and greatly increased pervasive transcription in both yeast and mESCs.

Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses.

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

A Gaussian-process approximation to a spatial SIR process using moment closures and emulators.

The dynamics that govern disease spread are hard to model because infections are functions of both the underlying pathogen as well as human or animal behavior. This challenge is increased when modeling how diseases spread between different spatial locations. Many proposed spatial epidemiological models require trade-offs to fit, either by abstracting away theoretical spread dynamics, fitting a deterministic model, or by requiring large computational resources for many simulations. We propose an approach that approximates the complex spatial spread dynamics with a Gaussian process. We first propose a flexible spatial extension to the well-known SIR stochastic process, and then we derive a moment-closure approximation to this stochastic process. This moment-closure approximation yields ordinary differential equations for the evolution of the means and covariances of the susceptibles and infectious through time. Because these ODEs are a bottleneck to fitting our model by MCMC, we approximate them using a low-rank emulator. This approximation serves as the basis for our hierarchical model for noisy, underreported counts of new infections by spatial location and time. We demonstrate using our model to conduct inference on simulated infections from the underlying, true spatial SIR jump process. We then apply our method to model counts of new Zika infections in Brazil from late 2015 through early 2016.

RNA-sequencing exploration on SIR2 and SOD genes in Polyalthia longifolia leaf methanolic extracts (PLME) mediated anti-aging effects in Saccharomyces cerevisiae BY611 yeast cells.

Polyalthia longifolia is well-known for its abundance of polyphenol content and traditional medicinal uses. Previous research has demonstrated that the methanolic extract of P. longifolia leaves (PLME, 1 mg/mL) possesses anti-aging properties in Saccharomyces cerevisiae BY611 yeast cells. Building on these findings, this study delves deeper into the potential antiaging mechanism of PLME, by analyzing the transcriptional responses of BY611 cells treated with PLME using RNA-sequencing (RNA-seq) technology. The RNA-seq analysis results identified 1691 significantly (padj < 0.05) differentially expressed genes, with 947 upregulated and 744 downregulated genes. Notably, the expression of three important aging-related genes, SIR2, SOD1, and SOD2, showed a significant difference following PLME treatment. The subsequent integration of these targeted genes with GO and KEGG pathway analysis revealed the multifaceted nature of PLME's anti-aging effects in BY611 yeast cells. Enriched GO and KEGG analysis showed that PLME treatment promotes the upregulation of SIR2, SOD1, and SOD2 genes, leading to a boosted cellular antioxidant defense system, reduced oxidative stress, regulated cell metabolism, and maintain genome stability. These collectively increased longevities in PLME-treated BY611 yeast cells and indicate the potential anti-aging action of PLME through the modulation of SIR2 and SOD genes. The present study provided novel insights into the roles of SIR2, SOD1, and SOD2 genes in the anti-aging effects of PLME treatment, offering promising interventions for promoting healthy aging.

SIRT6 positively regulates antiviral response in a bony fish, the Chinese perch Siniperca chuatsi.

SIRT6, a key member of the sirtuin family, plays a pivotal role in regulating a number of vital biological processes, including energy metabolism, oxidative stress, and immune system modulation. Nevertheless, the function of SIRT6 in bony fish, particularly in the context of antiviral immune response, remains largely unexplored. In this study, a sirt6 was cloned and characterized in a commercial fish, the Chinese perch (Siniperca chuatsi). The SIRT6 possesses conserved SIR2 domain with catalytic core region when compared with other vertebrates. Tissue distribution analysis indicated that sirt6 was expressed in all detected tissues, and the sirt6 was significantly induced following infection of infectious haemorrhagic syndrome virus (IHSV). The overexpression of SIRT6 resulted in significant upregulation of interferon-stimulated genes (ISGs), such as viperin, mx, isg15, irf3 and ifp35, and inhibited viral replication. It was further found that SIRT6 was located in nucleus and could enhance the expression of ISGs induced by type I and II IFNs. These findings may provide new information in relation with the function of SIRT6 in vertebrates, and with viral prevention strategy development in aquaculture.

The relationship between systemic inflammatory response, screen detection and outcome in colorectal cancer.

AIM: A raised systemic inflammatory response correlates with poorer colorectal cancer (CRC) outcomes. Faecal immunochemical test bowel screening aims to detect early-stage disease. We assessed the relationship between systemic inflammatory response, screen detection and CRC survival. METHOD: A retrospective, observational cohort study compared screen-detected and non-screen-detected CRC patients undergoing resection. Systemic inflammatory response was measured using lymphocyte/monocyte, neutrophil/lymphocyte and platelet/lymphocyte ratios (LMR, NLR, PLR). Covariables were compared using χ2 testing and survival with Cox regression. RESULTS: A total of 761 patients were included (326 screen-detected, 435 non-screen-detected). Screen-detected patients had lower systemic inflammatory response: low (<2.4) LMR (28.8% vs. 44.6%; P < 0.001), moderate (3-5) or high (>5) NLR (26.1% vs. 30.6%, P < 0.001; and 7.7% vs. 19.5%, P < 0.001) and high (>150) PLR (47.2% vs. 64.6%; P < 0.001). Median follow-up was 63 months. On univariate analysis, non-screen detection (hazard ratio [HR] 2.346, 95% CI 1.687-3.261; P < 0.001), advanced TNM (P < 0.001), low LMR (HR 2.038, 95% CI 1.514-2.742; P < 0.001), moderate NLR (HR 1.588, 95% CI 1.128-2.235; P = 0.008), high NLR (HR 2.382, 95% CI 1.626-3.491; P < 0.001) and high PLR (HR 1.827, 95% CI 1.326-2.519; P < 0.001) predicted poorer overall survival (OS). Non-screen detection (HR 2.713, 95% CI 1.742-4.226; P < 0.001), TNM (P < 0.001), low LMR (HR 1.969, 95% CI 1.340-2.893; P < 0.001), high NLR (HR 2.368, 95% CI 1.448-3.875; P < 0.001) and high PLR (HR 2.110, 95% CI 1.374-3.240; P < 0.001) predicted poorer cancer-specific survival (CSS). On multivariate analysis, non-screen detection (HR 1.698, 95% CI 1.152-2.503; P = 0.008) and low LMR (HR 1.610, 95% CI 1.158-2.238; P = 0.005) independently predicted poorer OS. Non-screen detection (HR 1.847, 95% CI 1.144-2.983; P = 0.012) and high PLR (HR 1.578, 95% CI 1.018-2.444; P = 0.041) predicted poorer CSS. CONCLUSION: Screen-detected CRC patients have a lower systemic inflammatory response. Non-screen detection and systemic inflammatory response (measured by LMR and PLR respectively) were independent predictors of poorer OS and CSS.

A Coupled Statistical and Deterministic Model for Forecasting Climate-Driven Dengue Incidence in Selangor, Malaysia.

The mosquito-borne dengue virus remains a major public health concern in Malaysia. Despite various control efforts and measures introduced by the Malaysian Government to combat dengue, the increasing trend of dengue cases persists and shows no sign of decreasing. Currently, early detection and vector control are the main methods employed to curb dengue outbreaks. In this study, a coupled model consisting of the statistical ARIMAX model and the deterministic SI-SIR model was developed and validated using the weekly reported dengue data from year 2014 to 2019 for Selangor, Malaysia. Previous studies have shown that climate variables, especially temperature, humidity, and precipitation, were able to influence dengue incidence and transmission dynamics through their effect on the vector. In this coupled model, climate is linked to dengue disease through mosquito biting rate, allowing real-time forecast of dengue cases using climate variables, namely temperature, rainfall and humidity. For the period chosen for model validation, the coupled model can forecast 1-2 weeks in advance with an average error of less than 6%, three weeks in advance with an average error of 7.06% and four weeks in advance with an average error of 8.01%. Further model simulation analysis suggests that the coupled model generally provides better forecast than the stand-alone ARIMAX model, especially at the onset of the outbreak. Moreover, the coupled model is more robust in the sense that it can be further adapted for investigating the effectiveness of various dengue mitigation measures subject to the changing climate.

R 0 May Not Tell Us Everything: Transient Disease Dynamics of Some SIR Models Over Patchy Environments.

This paper examines the short-term or transient dynamics of SIR infectious disease models in patch environments. We employ reactivity of an equilibrium and amplification rates, concepts from ecology, to analyze how dispersals/travels between patches, spatial heterogeneity, and other disease-related parameters impact short-term dynamics. Our findings reveal that in certain scenarios, due to the impact of spatial heterogeneity and the dispersals, the short-term disease dynamics over a patch environment may disagree with the long-term disease dynamics that is typically reflected by the basic reproduction number. Such an inconsistence can mislead the public, public healthy agencies and governments when making public health policy and decisions, and hence, these findings are of practical importance.

Final epidemic size of a two-community SIR model with asymmetric coupling.

Communities are commonly not isolated but interact asymmetrically with each other, allowing the propagation of infectious diseases within the same community and between different communities. To reveal the impact of asymmetrical interactions and contact heterogeneity on disease transmission, we formulate a two-community SIR epidemic model, in which each community has its contact structure while communication between communities occurs through temporary commuters. We derive an explicit formula for the basic reproduction number R 0 , give an implicit equation for the final epidemic size z, and analyze the relationship between them. Unlike the typical positive correlation between R 0 and z in the classic SIR model, we find a negatively correlated relationship between counterparts of our model deviating from homogeneous populations. Moreover, we investigate the impact of asymmetric coupling mechanisms on R 0 . The results suggest that, in scenarios with restricted movement of susceptible individuals within a community, R 0 does not follow a simple monotonous relationship, indicating that an unbending decrease in the movement of susceptible individuals may increase R 0 . We further demonstrate that network contacts within communities have a greater effect on R 0 than casual contacts between communities. Finally, we develop an epidemic model without restriction on the movement of susceptible individuals, and the numerical simulations suggest that the increase in human flow between communities leads to a larger R 0 .

Wording the trajectory of the three-year COVID-19 epidemic in a general population - Belgium.

The trajectory of COVID-19 epidemic waves in the general population of Belgium was analysed by defining quantitative criteria for epidemic waves from March 2020 to early 2023. Peaks and starting/ending times characterised nine waves numerated I to IX based on the daily reported incidence number (symbol INCID) and three "endemic" interval periods between the first four waves. The SIR compartmental model was applied to the first epidemic wave by fitting the daily prevalence pool (symbol I) calculated as the sum of the daily incidence rate and estimated number of subjects still infectious from the previous days. The basic reproductive number R0 was calculated based on the exponential growth rate during the early phase and on medical literature knowledge of the time of generation of SARS-CoV-2 infection. The first COVID-19 wave was well fitted by an open SIR model. According to this approach, dampened recurrent epidemic waves evolving through an endemic state would have been expected. This was not the case with the subsequent epidemic waves being characterised by new variants of concern (VOC). Evidence-based observations: 1) each epidemic wave affected less than a fifth of the general population; 2) the Vth epidemic wave (VOC Omicron) presented the greatest amplitude. The lack of recurrence of the same VOC during successive epidemic waves strongly suggests that a VOC has a limited persistence, disappearing from the population well before the expected proportion of the theoretical susceptible cohort being maximally infected. Fitting the theoretical SIR model, a limited persistence of VOCs in a population could explain that new VOCs replace old ones, even if the new VOC has a lower transmission rate than the preceding one. In conclusion, acquisition of potential defective mutations in VOC during an epidemic wave is a potential factor explaining the absence of resurgence of a same VOC during successive waves. Such an hypothesis is open to discussion and to rebuttal. A modified SIR model with epidemic waves of variable amplitude related not only to R0 and public health measures but also to acquisition of defective fitting in virus within a population should be tested.